Abstract
We present exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse squared potential in arbitrary dimensions. The ladder operators for the radial wavefunctions are established by the factorization method. We find that those operators together with satisfy the commutation relation of the generators of an su(1, 1) algebra. Some comments are made on the general calculation formula for off-diagonal matrix elements and the recurrence relation among them. Also, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r → ir.
| Original language | English |
|---|---|
| Article number | 008 |
| Pages (from-to) | 173-177 |
| Number of pages | 5 |
| Journal | Physica Scripta |
| Volume | 73 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Feb 2006 |
| Externally published | Yes |